Step-by-Step Solution
Key Concept: Split $7x = 2x + 5x$ since $\sqrt{2} \times 5\sqrt{2} = 10$.
$\sqrt{2}x^2 + 2x + 5x + 5\sqrt{2} = 0 \Rightarrow \sqrt{2}x(x + \sqrt{2}) + 5(x + \sqrt{2}) = 0$.
$(\sqrt{2}x + 5)(x + \sqrt{2}) = 0$. [1.0 Mark]
Roots are $x = -5/\sqrt{2} = -5\sqrt{2}/2$ and $x = -\sqrt{2}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Factoring into $(\sqrt{2}x + 5)(x + \sqrt{2}) = 0$: 1.0 Mark
Finding roots $-5/\sqrt{2}$ and $-\sqrt{2}$: 1.0 Mark
Correct Answer: